I think it is kind of a fact actually. They would not be making Hardware any more has it not been for their own games. Think of the SNES/Genesis era. Was a true war. They did not continue on by putting out a less bloodier version of Mortal Kombat. Donkey Kong Country, Mario games, and on and on.

N64, sure they had a few big third parties due to mostly RARE, which they had a partnership with, but not much.

There are some exceptions to the rule, systems that are just popular with the general public such as the Wii, NES and Switch, but it almost always has to do with the games by Nintendo. Even the Wii's largest initial selling point was Wii Sports. Again, a Nintendo game though. Motion control in general was nothing spectacular, but it helped interest many people.

Ever since the SNES days, third party games have almost always been second to Nintendo, be it the aforementioned Mortal Kombat being less bloody or all the watered down ports of third party games due to system strength. It is Nintendo games first and that is why they make hardware. Third party games are just there to attract people who may not buy a system for a few games, or filler. Best of both worlds.

Unfortunately, fact

As others have pointed is a bit of a mix of both. Theres some credit to the allegations, even tho its not strictly 100% truthful.

The most boring answers are the simplest ones sometimes.
It's both. You already underlined it most recently with the Switch, Nintendo did take their time to survey 3rd party for needed features, which lead to the increase of RAM size to 4GB. Maybe they did not think it necessary for their own use, at the time.
There's a clear willingness to not only corner themselves with hardware features that would only find purpose exclusively with their own games.

At worse, considering their driving philosophy when it comes to hardware evolution and new methods of play, it also shows to the industry, that there's more possibilities to exploit than the standard gameplay layout, motion control and gyro aiming are big proposants of that.

I'd agree that it's a yes and no-answer. Nintendo considers what 3rd party publishers have to say and what they want (although that doesn't necessarily translate into the final system). I'm sure Nintendo has its desires in what it wants from its hardware as well (they're making it after all).

Or maybe the third party games Nintendo tends to focus on are quite different from that of Sony/Microsoft?

It's complicated.
Here's an excerpt from the making of the Nintendo GameCube
"Miyamoto spoke on the challenges of Nintendo 64 development and the transition from 2D to 3D game development. He believed that the struggles some third parties faced during the N64 era were necessary because it forced weaker developers out of the industry and made the remaining developers much stronger.

“It was hard to develop for the Nintendo 64, especially because the software libraries were delayed. However, the Nintendo 64 truly brought developers into the era of 3D, and there were bound to be problems with that,” says Miyamoto. ” I suppose developers who have been working with pseudo-3D on the PlayStation, are now finding themselves playing catch-up working in real 3D on the PlayStation 2. In that sense, I think the PlayStation 2 is even harder to develop for than the Nintendo 64. Nintendo 64 weeded out weaker developers at an early stage. In the long term, I think that was necessary. Almost a rite of passage.”
“Nintendo’s position is that we are going to sell our hardware with our own software titles, and if consumers buy a number of Gamecubes, then licensees would become interesting in making games for Nintendo Gamecube. That’s the general idea in Nintendo’s business. So we are not actually approaching them [third parties] and asking them to make software for Nintendo. Already there are a number of requests [from publishers] who would like to make the software for Gamecube, so probably in September we will start explaining the technology and delivering the development kits to them. Once again, it’s their decision. If they would like to make Gamecube software, that’s fine, but we will never demand them to make games for Gamecube.”

I find it interesting that Miyamoto says PS2 is probably harder to develop for than N64. And while that may have been true (somebody correct me if it wasn't), PS2 had more economical software prices and storage thanks to its DVD (like the PS1's CD over the N64 cartridge) and developers and publishers couldn't get enough of PS2. Tough to develop for is not synonymous with a lack of games. PS3 was tough to develop for but once it got older and Slim, the games came in big numbers (at least thanks to digital distribution).
Nintendo makes their hardware with their own software in mind, and that hasn't changed on Switch. However, we do see a willingness with Switch to listen to devs and publishers in the development process. As you mentioned, Nintendo was going to ship Switch with a measly 2 GB RAM, but Capcom helped convince them otherwise.
Sony and Microsoft usually make their consoles with all manners of publishers in mind, Nintendo usually looks inward.

The GameCube was interesting in that Nintendo sought to make an easier console to develop for, but they were still operating under the assumption that third parties should come to them after they've sold enough systems. This was still Yamauchi's Nintendo at the time, so there were still some burned bridges with companies like Square and Capcom.

In recent times though, Nintendo has been much more proactive in involving third party input when developing hardware. Especially with the Switch, given that it's general producer, Yoshiaki Koizumi, comes from an art and graphics background. So you can see that influence in how the Switch was designed by prioritizing common middleware tools, various clock profiles, and leveraging Nvidia's graphics library.

Of course, Nintendo will always design systems for their own needs before anything else, but this idea that they're ignorant or neglectful of the needs of third parties hasn't been true for a long time.

Actually no, but the result can be similar.

Nintendo follows an idea about games. These ideas come from in-house and they produce games following their ideas. With the NES/SNES and to some extent N64 the 3rd-party producers were following the blueprints Nintendo layed out, which is why there are significant 3rd-party games on these consoles. But later on the game industry started to follow more mainstream trends and dismiss the blueprints Nintendo layed out. There are exceptions, Just Dance for instance followed Nintendo and refined the concept and is now a staple of the video gam eindustry making a lot of money. But as nowadays most 3rd-parties just follow the mainstream trends often Nintendo is the only taking advantage of their consoles features. Thus the impression theys make their consoles only for their games.

I do have to question if that's the wrong questions. The companies that produce the consoles and launchers (Switch, Playstation, Xbox, Steam, somewhat Epic, Apple, etc) should dictate what the industry does, not the third parties whose products are meant to be played on them.